Remarks on the Dirac oscillator in $(2+1)$ dimensions

Abstract

In this work the Dirac oscillator in $(2+1)$ dimensions is considered. We solve the problem in polar coordinates and discuss the dependence of the energy spectrum on the spin parameter $s$ and angular momentum quantum number $m$. Contrary to earlier attempts, we show that the degeneracy of the energy spectrum can occur for all possible values of $sm$. In an additional analysis, we also show that an isolated bound state solution, excluded from Sturm-Liouville problem, exists.

arXiv comment5 pages, 2 figures, minor corrections, published version

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• The influence of Aharonov-Casher effect on the generalized Dirac oscillator in the cosmic string space-time
• Relativistic quantum dynamics of neutral particle in external electric fields: An approach on effects of spin
• Quantum dynamics of a spin-1/2 charged particle in the presence of magnetic field with scalar and vector couplings
• Effects of quantum deformation on the Jaynes-Cummings and anti-Jaynes-Cummings models
• Emergent topological fields and relativistic phonons within the thermoelectricity in topological insulators
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• Bound-state solutions for the charged Dirac oscillator in a rotating frame in the Bonnor-Melvin-Lambda spacetime